Many computer-based applications exist for aiding in the design of products. Using these applications, an engineer can construct a computer model of a particular product and can analyze the behavior of the product through various analysis techniques. Further, certain analytical tools have been developed that enable engineers to evaluate and test multiple design configurations of a product.
For example, a blade and disk assembly may be modeled for design purposes. The blade and disk assembly may be initially modeled with certain simplifying assumptions made, such as the assumption that the connection between the blade and the disk is a rigid connection with no flexibility. An analytical tool, such as, for example, a finite element analysis (FEA) application, may test design configurations of the blade and disk assembly, and for the interconnection at the blade root, against requirements relating to stress and strain, vibration response, modal frequencies, and stability to predict the failure and fatigue life of the assembly in terms of specific design parameters. The data from the analytical tool may then be used to provide insight on how specific design parameters of the assembly can be modified to increase the fatigue life of the various components.
A blade used in turbomachinery is subject to significant sources of vibrations, which can lead to failure. Numerical models using modal analysis are traditionally used to evaluate the propensity of a blade to fail in vibration. Modal analysis is quick and efficient, but has the disadvantage of over-simplifying the connection between the blade and the disk. As a result, the numerical results derived from modal analysis, such as harmonic response and related techniques, are of limited usefulness for areas at or near the connection between the blade and the disk. Analyzing or predicting the modes of failure encountered at or near the blade root, such as wear, fretting, cracks due to high cycle fatigue, etc., requires a different approach that establishes a model in the time domain, and applies transient analysis. A traditional approach for transient analysis would apply a theoretical or actual forcing function to the blade, and then simulate many cycles until the vibration reaches a steady-state regime. The behavior inside the contact area at the blade root could then be analyzed.
Several drawbacks result from the traditional approach. For example, the classical approach to transient analysis, including simulating many cycles until the vibration reaches a steady-state regime, is extremely computer intensive. The forcing function to be applied to the blade is also typically of such complexity that it needs to be either simplified or idealized. Another problem is that the non-linear nature of behavior at the connection between the blade and the disk may introduce unintended frequency content into the response, preventing the emergence of a steady-state condition and complicating any interpretation of the results of the transient analysis.
The method of the present disclosure is directed towards improvements to existing technology.